Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 5x - 9$ and $ KL = 6x - 15$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {5x - 9} = {6x - 15}$ Solve for $x$ $ -x = -6$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 5({6}) - 9$ $ KL = 6({6}) - 15$ $ JK = 30 - 9$ $ KL = 36 - 15$ $ JK = 21$ $ KL = 21$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {21} + {21}$ $ JL = 42$